1. Field of the Invention
The present invention is in the field of telecommunications and, in particular, in the field of equalization in a multiple input scenario, in which a receiver receives signals from more than one transmit antenna.
2. Description of Related Art
The steadily-increasing demand for high data rates necessary for todays and future mobile radio applications requires high data rate transmission techniques efficiently exploiting the available bandwidth or, in other words, the achievable channel capacity. Therefore, multiple input multiple output (MIMO) transmission systems have achieved considerable importance in recent years. MIMO systems employ a plurality of transmitting points, each of the transmitting points having a transmit antenna, and a plurality of receiving points, each of the receiving points having a receiving antenna, for receiving signals being transmitted by the multiple transmitting points through different communication channels.
For example, an enormous capacity increase can be achieved on a multiple input multiple output channel in rich scattering environments. The capacity increase is linear with a number of transmit antennas unless it exceeds a number of receive antennas. In order to enable highly reliable communications in such a system, maximum-likelihood detection would be the optimum way, however, as the number of transmit antennas increases, the complexity of the receiver becomes prohibitive.
The increasing receiver complexity with increasing number of transmit antennas results from an increasing number of communication channels to be taken into account in order to detect the information transmitted by the number of transmit antennas from a signal received by a further number of receive antennas. In P. W. Wolniansky, G. J. Foschini, G. D. Golden and R. A. Valenzuela, “V-Blast: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel”, in URSI International Symposium on Signals, Systems, and Electronics, September 1998, pp. 295-300, a vertical bell labs layered space-time (V-Blast) detection scheme with lower complexity is disclosed. Independent data streams associated with different transmit antennas, called layers, are detected at a receiver by nulling out interference of other layers from each other in a successive manner.
Moreover, it was suggested, to perform an optimum detection ordering which is of great importance for the successive interference cancellation, whereby, at each detection stage, a transmit signal value estimate associated with a smallest estimation error is provided.
The V-Blast detection scheme mentioned above calculates the nulling vector based on a zero forcing (ZF) criterion. S. Böro, G. Bauch, A. Pavlic, and A. Semmerl. “Improving BLAST Performance using Space-Time Block Codes and Turbo Decoding,” in Proc. IEEE Global Telecommunications Conference (GLOBECOM 2000), vol. 2, November/December 2000, pp. 1067-1071 and A. Benjebbour, H. Murata, and S. Yoshida. “Comparison of Ordered Successive Receivers for Space-Time Transmissions,” in Proc. IEEE Vehicular Technology Conference (VTC 2001-Fall), Atlantic City, USA, October 2001, pp. 2053-2057, disclose detection schemes where a minimum mean square error (MMSE) criterion is adapted to the V-Blast architecture improving the performance. These detection schemes require calculation of either pseudo inverse (ZF V-Blast) or inverse (MMSE V-Blast) of a matrix at each detection stage, i.e., at every step of layer detection, which is still computationally expensive and prohibitive for large number of data streams. Therefore, the estimation complexity associated with the above-mentioned detection schemes is enormous.
For the ZF criterion, a reduction of complexity is possible. In D. Wübben, R. Böhnke, J. Rinas, V. Kühn and K. D. Kammeyer, “Efficient Algorithm for Decoding Layered Space-Time Codes,” IEE Electronics Letters, vol. 37, no. 22, pp. 1348-1350, October 2001 and in D. Wübben, J. Rinas, R. Böhnke, V. Kühn and K. D. Kammeyer, “Efficient Algorithm for Decoding Layered Space-Time Codes,” in Proc. Of 4. ITG Conference on Source and Channel Coding, Berlin, January 2002, pp. 399-405, computational reduction schemes are proposed which are based on QR decomposition with suboptimum detection ordering.
In W. Zha and S. D. Blostein, “Modified Decorrelating Decision-Feedback Detection of BLAST Space-Time System,” in Proc. IEEE Int. Conference on Communications (ICC 2002), vol. 1, New York, USA, April/May 2002, pp. 335-339 discloses a Cholesky factorization which is utilized with reordering by unitary transformation at every detection stage leading to optimum ordering.
A similar contribution based on QR decomposition for MMSE criterion is disclosed in R. Böhnke, D. Wübben, V. Kühn, and K. D. Kammeyer, “Reduced Complexity MMSE Detection for BLAST Architecture,” in Proc. IEEE Global Telecommunications Conference (GLOBECOM 2003), vol. 4, San Francisco, USA, December 2003, pp. 2258-2262. The ordering disclosed therein is suboptimum which leads to an increased detection error.
In B. Hassibi, “An Efficient Square-Root Algorithm for BLAST,” in Proc. IEEE Int. Conference on Acoustics, Speech, and Signal Processing. (ICASSP'00), vol. 2, Istanbul, June 2000, pp. II737-II740, a unitary transformation is disclosed for reordering. In E. Biglieri, G. Taricco and A. Tulino, “Decoding Space-Time Codes With BLAST Architectures,” IEEE Transactions on Signal Processing, vol. 50, no. 10, pp. 2547-2552, October 2002, a Cholesky factorization is disclosed which, however, does not involve an ordering strategy and, therefore, does not lead to an optimum performance.
In other words, the prior art approaches disclose either a reduction of complexity associated with a suboptimum detection ordering, which leads to an increased estimation error, or an optimum reordering for reduction of the estimation error at a cost of an increased complexity.
FIG. 10 shows a system model of MIMO channel. The system is equipped with NT transmit antennas and NR receive antennas, where NT≦NR. In the following, it is assumed, that the signals are narrow band so that a non-dispersive fading channel is present. Moreover, FIG. 10 shows a discrete time system model in an equivalent complex baseband.
The channel inputs xi, i=1, . . . , NT are complex valued baseband signals and are transmitted from NT antennas simultaneously. In other words, each transmit antenna transmits a channel input value of the channel input sequence. The channel tap gain from transmit antennas i to receive antenna j is denoted by hj,i.
These channel taps are independent zero mean complex Gaussian variables of equal variance E[|hj,i|2]=1. This assumption of independent paths holds if antenna spacing is sufficiently large and if the system is surrounded by rich scattering environment. The signal at receive antenna j can be expressed by
            y      j        =                            ∑                      i            =            1                                N            T                          ⁢                              h                          j              ,              i                                ⁢                      x            i                              +              n        j              ,where y=Hx+n is an additive noise at receive antenna j. By collecting the receive signal values determined by the above equation for NR receive antennas, the receive signals can be concisely expressed in matrix formy=Hx+njwhere
      H    =          [                                                  h                              1                ,                1                                                          ⋯                                              h                              1                ,                                  N                  T                                                                                          ⋮                                ⋰                                ⋮                                                              h                                                N                  R                                ,                1                                                          ⋯                                              h                                                N                  R                                ,                                  N                  T                                                                        ]        ,y=[y1, . . . , yNR]T, x=[x1, . . . , xNT]T, n=[n1, . . . , nNR]T, and (•)T denotes transposition.
FIG. 11 demonstrates a detection procedure of V-Blast. The receive signal y=y1, which is a vector, is filtered by a filter with coefficients fk1H to estimate the k1-th data stream which is the most reliable estimate among all NT entries of x, i.e., with minimum MSE at this first stage. The output is quantized by Q(•) and decision is made on xk1. Assuming that this decision is correct ({circumflex over (x)}k1=xk1), contribution of xk1 on the receive signal y1 is subtracted by multiplying xk1 with the corresponding channel impulse response hk1, which is a vector, which is the k1-th column of H. This procedure is repeated NT times until all the entries of x are detected.
In the following, a detailed filter calculation and ordering strategy according to the above prior art approach will be described.
An error signal of a linear filter FH is expressed asε=FHy−x.
The linear MMSE filter can be found by applying an orthogonality by principle, i.e., E[εyH]=0. From the above equations, a solution is given byFH=ΦxxHH(HΦxxHH+Φnn)−1,where covariance matrices of channel input and noise are defined asΦxx=E[xxH]undΦnn=E[nnH].
Assuming that the covariance matrices in the above equation are invertible, the above equation for the linear filter may be represented in an alternative form
      F    H    =                    (                              Φ            xx                          -              1                                +                      H            ⁢                                                  ⁢                          Φ              nn                              -                1                                      ⁢                          H              H                                      )                    -        1              ⁢          H      H        ⁢          Φ      nn              -        1            where the known matrix inversion lemma has twice been applied to obtain the above equation. From the above, the error covariance matrix reads as
      Φ    εε    =            E      ⁡              [                              ∈∈                    H                ]              =                            (                                    Φ              xx                              -                01                                      +                                          H                H                            ⁢                              Φ                nn                                  -                  1                                            ⁢              H                                )                          -          1                    .      
It is to be noted that the diagonal entries of Φεε are MSE, i.e., E[|xi−{circumflex over (x)}i|2], i=1, . . . , NT. Thus, the k1-th data stream having the minimum diagonal entry of Φεε can be seen as the most reliable one in the MMSE sense and must be detected at the first stage in order to avoid error propagation, which corresponds to the optimum ordering mentioned above.
The corresponding filter fk1H corresponds to the k1-th row of FH. At the second stage, since k1-th entry of x has been detected, the k1-th column of the channel matrix H can be neglected, leading to an updated system only with NT−1 transmit antennas.
In order to generalize the procedure, a deflated channel matrix H(i) is introduced where columns k1, . . . , ki−1 of H are replaced by zeros for i=2, . . . , NT and H(1)Δ=H. At i-th stage, Φεε(i) and F(i),H are calculated from the above equations by replacing H with H(i). Then, the optimum detection scheme can be described as
            k      i        =                  argmin                  k          ∉                      {                                          k                i                            ,                                                          ⁢              …              ⁢                                                          ,                              k                                  i                  -                  1                                                      }                              ⁢              e        k        T            ⁢              Φ                  ∈          ∈                          (          i          )                    ⁢              e        k                                f                  k          i                H            =                                    e                          k              i                        T                    ⁢                      F                                          (                i                )                            ,              H                                      =                              e                          k              i                        T                    ⁢                      Φ                          ∈              ∈                                      (              i              )                                ⁢                      H            H                    ⁢                      Φ            nn                          -              1                                            ,  where ek is the k-th column of an identity matrix of size NT and the last step follows from the equations mentioned above. Therefore, MMSE-V-Blast repeats the procedure and requires matrix inverse calculations NT times for each receive sequence, which is computationally expensive. In other words, the above-discussed detection scheme applies an optimum ordering, so that a resulting estimation error is reduced. This error reduction is however, associated with an enormous computational complexity.
In E. Bigliei, g. Taricco and A. Tulino, “Decoding Space-Time Codes With BLAST Architectures,” IEEE Transactions on Signal Processing, vol. 50, no. 10, pp. 2547-2552, October 2002, and in G. Ginis and J. M. Cioffi, “On the Relation Between V-BLAST and the GDFE,” IEEE Communications Letters, vol. 5, no. 9, pp. 364-366, September 2001, the V-Blast architecture is described by a pair of forward and backward block filters with certain constraint on the backward filter structure. A resulting block diagram is shown in FIG. 12.
The sequence estimator shown in FIG. 12 comprises a forward filter 1201 having a number of inputs corresponding to a number of receive antennas, and a number of outputs coupled to a subtractor 1203. The subtractor 1203 has a number of outputs 1205 and a number of further inputs 1207. In other words, the filter 1201 is the previously mentioned forward filter. The number of outputs 1205 of the subtractor 1203 is coupled to a quantizer 1209 being operative for performing a hard decision. The quantizer has a number of outputs 1211 corresponding to the number of transmit antennas (or number of channel inputs). The number of outputs 1211 is fed back to a backward filter 1213 having a number of outputs corresponding to the number of receive antennas. The number of outputs of the backward filter 1213 is coupled to the number of further inputs 1207 of the subtractor 1203.
The estimate of a transmit sequence is provided via the number of outputs 1211 of the quantizer 1209. The estimates detected by the quantizer 1209 are filtered by the backward filter 1213, and filtered detected estimates are subtracted from filtered values provided by the forward filter 1201 in order to reduce intersymbol interferences. Therefore, the structure shown in FIG. 12 can be considered as a decision-feedback equalizer (DFE) structure, which is equivalent to the structure of FIG. 11.
The feedback filter BH must be unit lower (or upper) triangular so that the outputs of BH−1 are not subtracted from already detected signals. This is the causality constraint which is necessary to describe the successive interference cancellation procedure properly. In this context, a unit lower (upper) triangular matrix is a lower (upper) triangular matrix with one (“1”) values along the main diagonal.
However, the above-discussed approach suffers from the disadvantage, that there is no concern about detection ordering. In other words, the approach shown in FIG. 12 assumes that the detection ordering is already optimum, which is not the case all the time. Although the detection scheme associated with the structure shown in FIG. 12 has reduced complexity with respect to the estimation scheme of FIG. 11, it suffers from an increased estimation error in a case of a non-optimum decision ordering, i.e., in the case when the input sequence values are not reordered in such a way that the decision ordering is optimum.